Particular embodiments generally relate to voltage control oscillators (VCOs).
Unless otherwise indicated herein, the approaches described in this section are not prior art to the claims in this application and are not admitted to be prior art by inclusion in this section.
FIG. 1 depicts a conventional inductor/capacitor tank (LC tank) 100. LC tank 100 is formed by a parallel or series connection of an inductor 102 and a capacitor 104.
In operation, for a resonant frequency, the impedance of LC-tank 100 becomes infinite and when energy is stored initially in the tank, it circulates from voltage energy in capacitor 104 (½Cv2) to current energy in inductor 102 (½Li2), and vice versa. This exchange of energy occurs at the resonant frequency (½π√{square root over (LC)}), with the voltage and current being sinusoidal in quadrature phase with respect to each other and the ratio of the voltage and current amplitude being V0/I0=√{square root over (LC)}.
Reactive components, such as inductor 102 and capacitor 104, have losses in the real world implementation. The losses may be modeled as series or parallel resistances to LC-tank 100. An active circuit may be used to compensate for the losses. FIG. 2 depicts a conventional voltage controlled oscillator 200. The losses of LC-tank 100 are modeled as a resistance (RT) 202. The effect of the losses takes away energy from LC-tank 100, which dampens the oscillation making it fade away in time. Also, the losses are resistive in nature and generate noise that is usually represented as two orthogonal noise components: amplitude noise modulation (AM) and phase noise modulation (PM). The combination of these two orthogonal noise components and the sensitivity of the phase of oscillator 200 to these noise components results in phase noise around the resonance frequency, which degrades the spectral purity.
Regarding PM noise, the phase noise L in harmonic oscillators at an offset frequency Δω from the carrier can be expressed as:
            L      ⁡              (        Δω        )              =          10      ·              log        ⁡                  (                                                    ∑                i                            ⁢                                                          ⁢                              N                                  L                  ,                  i                                                                    2              ⁢                                                          ⁢                              Δω                2                            ⁢                              C                2                            ⁢                              A                2                                              )                      ,where A is the voltage oscillation amplitude across LC tank 100, C is LC tank capacitance, and, for white noise sources, NL,1, is given by:
            N              L        ,        i              =                  1                  T          0                    ⁢                        ∫          0          To                ⁢                                                            Γ                2                            ⁡                              (                t                )                                      ·                                                  ⁢                                                            i                                      n                    ,                    i                                    2                                ⁡                                  (                  t                  )                                            _                                ⁢                      ⅆ            t                                ,where T0 is the oscillation period,
            i              n        ,        i            2        ⁡          (      t      )        _is the white current noise power spectral density produced by the ith device, and Γi is the corresponding Impulse Sensitivity Function (TSF), representing the time-dependent sensitivity of the phase of the oscillation to in,i.
In VCOs, the TSF of the current noise sources in parallel to LC tank 100 may be a sinusoid in quadrature with the LC tank voltage, i.e., the VCO's phase noise sensitivity to these parallel current noise sources is max at the LC tank voltage zero crossing and minimum at the tank voltage peaks.
An active circuit 204 in oscillator 200 compensates for the losses by introducing a negative resistance (−R) 206 to sustain the oscillation at a desired frequency. However, active circuit 204 introduces noise that contributes to the total phase noise of oscillator 200.
FIG. 3 depicts a more detailed example of a conventional voltage controlled oscillator 200. LC-tank 100 (inductors 102a and 102b, and capacitor 104) is coupled to active circuit 204, which is represented as a cross-coupled transistor pair 302. Cross-coupled transistor pair 302 synthesizes negative resistance 206. As shown, cross-coupled transistor pair 302 is coupled in parallel to LC-tank 100 and includes a first transistor 304a (Mp) and a second transistor 304b (Mn).
The negative resistance synthesized by cross coupled transistor pair 302 is explained by describing the currents sourced/sinked by cross-coupled transistor pair 302 to/away from LC-tank 100. The current sourced/sinked is provided by a current source (Ibias) 306. When a voltage at a node Vp is at its positive peak value, a resistance RT 202 shown in FIG. 2 is taking away current from the node Vp. To compensate for this, transistor 304a is sourcing current into node Vp. When the voltage at node Vp is at its negative peak value, the resistance RT 202 of FIG. 2 is sourcing current into node Vp and transistor 304a is sinking current from node Vp. The dual behavior also happens at node Vn.
Cross-coupled transistor pair 302 is behaving as a negative resistance because cross-coupled transistor pair 302 is sourcing current from nodes Vp or Vn when the voltage is at a maximum at the nodes and sinking current from nodes Vp or Vn when the voltage is at a minimum at the nodes. The ratio between the voltage at nodes Vp or Vn to the current flowing out of nodes Vp or Vn is negative.
The current delivered to LC-tank 100 by cross-coupled transistor pair 302 has a square-like shape and a period of 1/(2πω0). FIG. 4 shows a graph 400 of an example of a square wave current delivered by cross-coupled transistor pair 302. The spectral content, which includes the fundamental frequency plus higher order harmonics, is filtered by a sine function. A graph 402 shows a frequency representation for the square wave current. For a 50% duty cycle of the square wave current that is delivered to LC-tank 100, the ratio between the current component delivered to LC-tank 100 at the fundamental frequency (Iω0) and the current delivered by current source 306 is calculated as follows:
      Ibias    =          I      0                  I      ⁢                          ⁢              ω        0              =                                                      (                                                                                          I                      0                                        π                                    ·                  sin                                ⁢                                  π                  2                                            )                        2                    +                                    (                                                                                          I                      0                                        π                                    ·                  sin                                ⁢                                  π                  2                                            )                        2                              =                                                                  (                                                      I                    0                                    π                                )                            2                        +                                          (                                                      I                    0                                    π                                )                            2                                      =                              2            ⁢                                                  ⁢                          I              0                                π                                        I        ⁢                                  ⁢                  ω          0                    Ibias        =          2      π      Only energy associated with the fundamental frequency contributes to the compensation of the resistance losses RT 202. From this, an intrinsic efficiency reduction factor of 2/π or −3.9 dB results.